This paper is a short review on Fock space based quantum probability and in particular, the theory of stop times based on it. The first section gives a short introduction to quantum probability discussing the notion of event, probability, random variables and their probability distributions pointing out the main differences with classical probability. The second section is devoted to the definition of Fock space quantum noises and their relationship with classical noises. Stop times, optional stopping and the strong Markov properties are studied in the least two sections. The author shows the fundamental definitions and points out the difficulties arising from noncommutativity.
The interested reader can find further results and recent developments on this subject in the papers K. B. Sinha, “Quantum stop times”, Quantum Probability and White Noise Analysis 12, 195–207 (2003; Zbl 1077.81523); S. Attal and A. Coquio, “Quantum stopping times and quasi-left continuity”, Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 4, 497–512 (2004; Zbl 1054.81025) and the references therein.